Rapid maneuvering of multi-body dynamic systems with optimal motion compensation

Abstract Rapid maneuvering of multi-body dynamical systems is an important, yet challenging, problem in many applications. Even in the case of rigid bodies, it can be difficult to maintain precise control over nominally stationary links if it is required to move some of the other links quickly because of the various nonlinearities and coupled interactions that occur between the bodies. Typical control concepts treat the multi-body motion control problem in two-stages. First, the nonlinear and coupling terms are treated as disturbances and a trajectory tracking control law is designed in order to attenuate their effects. Next, motion profiles are designed, based on kinematics parameterizations, and these are used as inputs to the closed loop system to move the links. This paper describes an approach for rapid maneuvering of multi-body systems that uses optimal control theory to account for dynamic nonlinearities and coupling as part of the motion trajectory design. Incorporating appropriate operational constraints automatically compensates for these multi-body effects so that motion time can be reduced while simultaneously achieving other objectives such as reducing the excitation of selected links. Since the compensatory effect is embedded within the optimal motion trajectories, the performance improvement can be obtained even when using simple closed-loop architectures for maneuver implementation. Simulation results for minimum time control of a two-axis gimbal system and for rapid maneuvering of a TDRS single-access antenna, wherein it is desired to limit the excitation of the satellite body to which the antenna is attached, are presented to illustrate the concepts.

[1]  Steven J. Rasmussen,et al.  Quantitative feedback theory: fundamentals and applications: C. H. Houpis and S. J. Rasmussen; Marcel Dekker, New York, 1999, ISBN: 0-8247-7872-3 , 2001, Autom..

[2]  E. Stoneking.  Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies , 2013 .

[3]  Zhuang Fu,et al.  Optimal feedback stabilization of a two-axis gimbaled system subject to saturation nonlinearity and multiple disturbances , 2014 .

[4]  R. Fuentes,et al.  Global analysis of the double-gimbal mechanism , 2008, IEEE Control Systems.

[5]  I. Michael Ross,et al.  Flight Implementation of Shortest-Time Maneuvers for Imaging Satellites , 2014 .

[6]  Sagar Bhatt,et al.  Overclock my satellite, sophisticated algorithms boost performance on the cheap , 2012 .

[7]  Hong Liu,et al.  Path planning for minimizing base reaction of space robot and its ground experimental study , 2009, 2009 International Conference on Mechatronics and Automation.

[8]  Ronald Zaleski,et al.  Attitude Control and Orbital Dynamics Challenges of Removing the First 3-Axis Stabilized Tracking and Data Relay Satellite from the Geosynchronous ARC , 2011 .

[9]  Adam G. Sears.  Design and experimental implementation of optimal spacecraft atntenna slews , 2013 .

[10]  Christian Smith,et al.  Robot manipulators , 2009, IEEE Robotics & Automation Magazine.

[11]  Gerd Hirzinger,et al.  Optimal motion planning for free-flying robots , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[12]  Qi Gong,et al.  Riemann–Stieltjes Optimal Control Problems for Uncertain Dynamic Systems , 2015 .

[13]  Eric Stoneking,et al.  Newton-Euler Dynamic Equations of Motion for a Multi-body Spacecraft , 2007 .

[14]  R. Y. Chiang,et al.  Robust antenna pointing control for TDRS spacecraft , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[15]  B. Ekstrand.  Equations of motion for a two-axes gimbal system , 2001 .

[16]  I. Michael Ross,et al.  A review of pseudospectral optimal control: From theory to flight , 2012, Annu. Rev. Control..

[17]  Mark Karpenko,et al.  Experimental Implementation of Riemann–Stieltjes Optimal Control for Agile Imaging Satellites , 2016 .

[18]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

[19]  Kai Chen,et al.  Optimal Path Planning for Minimizing Disturbance of Space Robot , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[20]  Xu Yang,et al.  Active disturbance rejection control for high pointing accuracy and rotation speed , 2009, Autom..

[21]  Bong Wie,et al.  Space Vehicle Dynamics and Control, Second Edition , 2008 .

[22]  Wei Kang,et al.  Zero-propellant maneuver guidance , 2009, IEEE Control Systems.

[23]  Robert Summers,et al.  PAYLOAD ON- ORBIT PERFORMANCE VERIFICATION OF TDRS HIJ , 2004 .

[24]  Chong-Ho Choi,et al.  Robust control of robot manipulator by model-based disturbance attenuation , 2003 .

[25]  Joseph Z. Ben-Asher,et al.  Minimum-time reorientation of a two-degree-of-freedom gyroscope , 1995 .